Measuring method and measuring device using quartz oscillator

ABSTRACT

An object of the present invention is that any of mass load, viscous load and viscoelasticity load is measured separately from other load whereby properties of the substance to be measured are able to be measured correctly. 
     The characteristic feature of the present invention is that, in a method where property of a substance contacting to a quartz oscillator equipped with electrodes on both sides of a quartz plate is measured on the basis of the changes in frequency of the above quartz oscillator, the property of the above substance is measured using at least two frequencies among the n-th overtone mode frequency (n=1, 3, 5, . . . (n=2k+1)) of quartz oscillator when voltage is applied between the above electrodes and using frequencies F 1 , F 2  (F 1 &lt;F 2 ) giving one half of the maximum value of conductance near the resonant point by each frequency.

TECHNICAL FIELD

The present invention relates to a measuring method and a measuringdevice using a quartz oscillator.

BACKGROUND ART

QCM (quartz crystal microbalance) has been widely used for themeasurement, etc. utilizing interaction and antigen-antibody reaction ofbiomaterials such as DNA and protein.

However, in the case of the conventional QCM, changes in resonancefrequency F_(s) are measured whereby a binding amount of a substance toa quartz oscillator is measured but, since the resonance frequency maybe affected by changes in viscosity and changes in viscoelasticity ofthe substance in addition to by mass load, those three elements have notbeen able to be measured separately.

DISCLOSURE OF THE INVENTION Problems that the Invention is to Solve

Under such circumstances, an object of the present invention is that anyof mass load, viscous load and viscoelasticity load is measuredseparately from other loads whereby properties of the substance to bemeasured are able to be measured correctly.

Means for Solving the Problems

In order to solve the above problems, the present inventor has obtainedthe following finding as a result of intensive studies.

From Martin's transmission theory (V. E. Granstaff, S. J. Martin, J.Appl. Phys., 1994, 75, 1319), changes in inductance Z when a substancehaving viscoelasticity is adhered to a quartz oscillator in a liquid isexpressed by the formula (1). In the formula, ω is angular frequency, ηis viscosity of the liquid, ρ is density of the liquid, h is filmthickness, G is shear modulus, G′ is storage elasticity and G″ is losselasticity.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 1} \right\rbrack & \; \\{Z = {{\left( {\omega\;\rho_{2}{\mu_{2}/2}} \right)^{1/2}\left( {1 + j} \right)} + {j\;\omega\;\rho_{1}h_{1}} + {\frac{\left( {G^{\prime} - {j\; G^{\prime\prime}}} \right)}{{G}^{2}}\omega^{2}\rho_{2}\eta_{2}h_{1}}}} & (1)\end{matrix}$

From the formula (1), changes in the resonance frequency F_(s) are asshown by the formula (2).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 2} \right\rbrack & \; \\{{\Delta\; F_{S}} = {{{Im}(Z)} = {{- \left( {\omega\;\rho_{2}{\eta_{2}/2}} \right)^{1/2}} - {\omega\;\rho_{1}h_{1}} + {\frac{\left( G^{\prime\prime} \right)}{{G}^{2}}\omega^{2}\rho_{2}\eta_{2}h_{1}}}}} & (2)\end{matrix}$

When the conductance by which the above resonance frequency F_(s) isresulted is G, the frequency where the conductance is one half (½ G)thereof is F₁, F₂ (F₁<F₂) (FIG. 1). Changing amount of this one-halffrequency (F₁−F₂)/2 is expressed by the formula (3).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 3} \right\rbrack & \; \\{{{\Delta\left( {F_{1} - F_{2}} \right)}/2} = {{{Re}(Z)} = {{- \left( {\omega\;\rho_{2}{\eta_{2}/2}} \right)^{1/2}} + {\frac{\left( G^{\prime} \right)}{{G}^{2}}\omega^{2}\rho_{2}\eta_{2}h_{1}}}}} & (3)\end{matrix}$

On the other hand, changes in another frequency F₂ are expressed by theformula (4) in view of the relation of F_(s)=(F₁+F₂)/2.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 4} \right\rbrack & \; \\{{\Delta\; F_{2}} = {{{- ~\omega}\;\rho_{1}h_{1}} + {\frac{\left( {G^{\prime} + G^{\prime}} \right)}{{G}^{2}}\omega^{2}\rho_{2}\eta_{2}h_{1}}}} & (4)\end{matrix}$

When G=G′+iG″=μ+iωη which is a Voight model being a model ofviscoelasticity of film is applied to G′ and G″ in the formula, theformula (4) and the formula (3) become as follows.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack & \; \\{{{\Delta\; F_{2}} = {{{- \omega}\;\rho_{1}h_{1}} + {\frac{\left( {\mu_{1} + {\omega\;\eta_{1}}} \right)}{\left( {\mu_{1}^{2} + {\omega^{2}\eta_{1}^{2}}} \right)}\omega^{2}\rho_{2}\eta_{2}h_{1}}}}{{Mass}\mspace{14mu}{Load}\mspace{14mu}{Viscoelasticity}\mspace{14mu}{Term}\mspace{14mu} 1}} & (5) \\\left\lbrack {{Formula}\mspace{14mu} 6} \right\rbrack & \; \\{{{{\Delta\left( {F_{1} - F_{2}} \right)}/2} = {{- \left( {\rho_{2}\eta_{2}{\omega/2}} \right)^{1/2}} - {\frac{\mu_{1}}{\left( {\mu_{1}^{2} + {\omega^{2}\eta_{1}^{2}}} \right)}\omega^{2}\rho_{2}\eta_{2}h_{1}}}}{{Viscous}\mspace{14mu}{load}\mspace{14mu}{Viscoelasticity}\mspace{14mu}{Term}\mspace{14mu} 2}} & (6)\end{matrix}$

Here, when expansion is done to an overtone of n-th (in which n=3, 5, .. . ) (when ω is a fundamental mode frequency, Nω is angular frequencyof n-th overtone mode frequency) with a proviso thatωη₁=Cμ₁  [Formula 7](in which C is a variable), the formulae (5) and (6) become as follows.Incidentally, F_(1N) and F_(2N) are frequencies (F₁ and F₂) whenresonance is done with n-th overtone mode frequency.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 7} \right\rbrack & \; \\{\mspace{79mu}{{\Delta\; F_{2\; N}} = {{{- N}\;\omega\;\rho_{1}h_{1}} + {\frac{\left( {1 + {CN}} \right)}{\mu_{1}\left( {1 + {C^{2}N^{2}}} \right)}N^{2}\omega^{2}\rho_{2}\eta_{2}h_{1}}}}} & (7) \\\left\lbrack {{Formula}\mspace{14mu} 8} \right\rbrack & \; \\{{{\Delta\left( {F_{1\; N} - F_{2N}} \right)}/2} = {{- \left( {\rho_{2}\eta_{2}N\;{\omega/2}} \right)^{1/2}} - {\frac{1}{\mu_{1}\left( {1 + {C^{2}N^{2}}} \right)}N^{2}\omega^{2}\rho_{2}\eta_{2}h_{1}}}} & (8)\end{matrix}$

Changes in frequency of overtone by mass load shows the changes in n-thovertone mode frequency of changing amount of frequency by mass load offundamental mode frequency and, therefore, when the difference betweenthe changing amount (ΔF₂₁) of mass load by fundamental mode frequencyand the changing amount (ΔF₂₃/3) of mass load by third overtone modefrequency or, in other words, (ΔF₂₁−ΔF₂₃/3) is determined, that is asshown by the formula (9).

Further, since changes in frequency of overtone by viscous load showsthe change of √n-times of changing amount of fundamental mode frequencyby viscous load, when the difference in changing amount of frequencybetween fundamental mode frequency and third overtone mode frequency(Δ(F₁−F₂)/2) or, in other words, ((F₁₁−F₂₁)/2−((F₁₃−F₂₃)/2√3) isdetermined, that is as shown by the formula (10).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 9} \right\rbrack & \; \\{{{{\Delta\; F_{21}} - {\Delta\;{F_{23}/3}}} = {\left\{ {\frac{\left( {1 + C} \right)}{\left( {1 + C^{2}} \right)} - \frac{3\left( {1 + {3C}} \right)}{\left( {1 + {9C^{2}}} \right)}} \right\}\frac{\omega^{2}\rho_{2}\eta_{2}h_{1}}{\mu_{1}}}}} & (9) \\\left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack & \; \\{{{{\Delta\left( {F_{11} - F_{21}} \right)}/2} - {{{\Delta\left( {F_{13} - F_{23}} \right)}/2}\sqrt{3}}} = {\left\{ {{- \frac{1}{\left( {1 + C^{2}} \right)}} + \frac{3\sqrt{3}}{\left( {1 + {9C^{2}}} \right)}} \right\}\frac{\omega^{2}\rho_{2}\eta_{2}h_{1}}{\mu_{1}}}} & (10)\end{matrix}$

When the measuring system solely comprises the mass load in the formula(9), the value of the right side is theoretically 0 while, when aviscoelasticity term 1 is contained, the value of the right side is thevalue of the viscoelasticity term 1.

It is also the same in the formula (10) that, when the measuring systemsolely comprises the viscous load therein, the value of the right sideis theoretically 0 while, when a viscoelasticity term 2 is contained,the value of the right side is the value of the viscoelasticity term 2.

Here, since the left sides of the formulae (9) and (10) are measuredvalues, (9)/(10) is a formula solely comprising a variable C whereby Cis able to be determined.

When C is determined, the term of

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 11} \right\rbrack & \; \\\frac{\omega^{2}\rho_{2}\eta_{2}h_{1}}{\mu_{1}} & \;\end{matrix}$is able to be resulted from the formula (9), the mass load term of theformula (7) is able to be determined and, when it is substituted for theformula (5), the viscoelasticity term 1 is also able to be determined.Similarly, the viscoelasticity load term of the formula (8) is also ableto be determined and, when the value is substituted for the formula (6),the viscoelasticity term 2 is also able to be determined. Accordingly,the viscoelasticity term 1 and mass load of the formula (5) are able tobe obtained. Similarly, the viscous load and viscoelasticity term 2 ofthe formula (6) are also able to be determined.

As such, separation of mass load, viscous load, viscoelasticity term 1and viscoelasticity term 2 were performed by the fundamental modefrequency and the third overtone mode frequency and, as shown in FIG. 2,a combination of at least two of the n-th overtone mode frequency (n=1,3, 5, . . . (n=2 k+1)) is able to be used whereby measurement is able tobe conducted by, for example, changing amount of frequency of thirdovertone mode frequency and fifth overtone mode frequency and,furthermore, by changing amount of frequency in plural combinations suchas that of fundamental mode frequency and fifth overtone mode frequencyand that of third overtone mode frequency and seventh overtone modefrequency. Incidentally, in measuring the changing amount of frequencyin plural combinations, the mean value of changing amounts of frequencyobtained in each combination is determined whereby it is possible tomake the error in each value little. In the case of three or morecombinations, it is also possible to use a least-squares method.

With regard to a model for viscoelasticity, although a Voight model wasused in this example, it is also possible to apply a Maxwell modelG=G′+iG″=μ+iη and other models.

On the basis of the above finding, the measuring method according to thepresent invention of first embodiment is that a method where property ofa substance contacting to a quartz oscillator equipped with electrodeson both sides of the quartz plate is measured on the basis of thevariation in frequency of the above quartz oscillator, characterized inthat, the property of the above substance is measured using at least twofrequencies among the n-th overtone mode frequency (n=1, 3, 5, . . .(n=2 k+1)) of the quartz oscillator when voltage is applied between theabove electrodes and using frequencies F₁, F₂ (F₁<F₂) giving one half ofthe maximum value of conductance near the resonant point by eachfrequency.

The present invention of second embodiment is that, its characteristicfeature is that, in the measuring method mentioned in first embodiment,any of mass load, viscous load and viscoelasticity load of the substanceis measured separately from other load by the difference in the changingamount of F₂ between the above frequencies (ΔF₂) and the difference inone half of the difference in F₁ and F₂ among the above frequencies(Δ(F₁−F₂)/2).

The measuring device according to the present invention of thirdembodiment is that, it is a measuring device using the measuring methodmentioned in second embodiment and its characteristic feature is thatthe difference in the changing amount of F₂ between each of the abovefrequencies (ΔF₂) and the difference of each one half of the differencein F₁ and F₂ among the above frequencies (Δ(F₁−F₂)/2) is expressed by agraph.

ADVANTAGES OF THE INVENTION

It is now possible in accordance with the present invention that, in themeasurement using a quartz oscillator, at least one of mass load,viscous load and viscoelasticity load of a substance which is an objectfor the measurement is able to be measured separately from other loadswhereby correct measure of the substance to be measured is able to beconducted.

BEST MODE FOR CARRYING OUT THE INVENTION

In the present invention, at least two frequencies among n-th overtonemode frequency (n=1, 3, 5, . . . (2 k+1)) are used. Incidentally,resonance frequency by the n-th overtone mode frequency also includesthe frequency near resonance frequency of the n-th overtone modefrequency and, for example, scanning of a range of about ±500 kHz isalso included.

In the measurement of changes in frequency, there is used a half-valuefrequency F₁, F₂ (F₁<F₂) giving a half-value conductance in a size ofone half of conductance where an oscillator is in a series resonancestate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph which shows the relation between resonance frequencyand conductance.

FIG. 2 is a graph which shows the relation between fundamental modefrequency and n-th overtone mode frequency.

FIG. 3 is an illustrative drawing of a biosensor device which is one ofthe embodiments of the present invention.

FIG. 4 is a plane view (a) and cross-sectional view (b) of a quartzoscillator of said device.

FIG. 5 is an illustrative drawing of constitution of said device.

FIG. 6 is an illustrative drawing of the cell of the biosensor device.

FIG. 7 is a graph which shows the measured result of an Example of thepresent invention.

FIG. 8 is a graph which shows another measured result of said Example.

FIG. 9 is a graph which shows another measured result of said Example.

EXPLANATION OF NUMERAL REFERENCES

-   -   1 biosensor device    -   2 sensor part    -   3 network analyzer    -   4 computer    -   5 cable    -   6 cable    -   7 quartz oscillator    -   8 crystal plate in circular shape    -   9 a the first gold electrode    -   10 a the second gold electrode    -   11 resin cover    -   12 reacting material    -   13 signal supplying circuit    -   14 measuring circuit    -   15 cell

As hereunder, one of the embodiments of the present invention will beillustrated by referring to the drawings. Incidentally, the presentinvention is not limited to the embodiments as such.

In FIG. 3, the numerical reference 1 shows a biosensor device which isone of the embodiments of the present invention.

This biosensor device 1 has a sensor part 2, a network analyzer 3 and acomputer 4. Each of the area between the sensor part 2 and the networkanalyzer 3 and the area between the network analyzer 3 and the computer4 is respectively connected by the cables 5, 6. The sensor part 2 isequipped with a quartz oscillator.

As shown in FIGS. 4( a) and (b) for its plane view and cross-sectionalview, the quartz oscillator equipped in the sensor part 2 is equippedwith the first gold electrode 9 a and the second gold electrode 10 a onthe surface side and the back side, respectively, of a crystal plate 8made of quartz in a circular shape. The gold electrodes 9 a, 10 a shownin the drawing are constituted in a circular shape and leading wires 9a, 10 b are connected thereto, respectively. As shown in FIG. 4 (b), thesecond gold electrode 10 a on the back side is covered by a resin cover11 whereby it is constituted in such a manner that, even in a statewhere the quartz oscillator 7 is placed in a solution, the second goldelectrode 10 a on the back side is not exposed to the solution andoscillation is still possible. On the other hand, the surface of thefirst gold electrode 9 a on the surface side is equipped with a reactionmaterial 12 which reacts with a specific component so as to adsorb saidcomponent and it contacts to the sample solution upon measurement.

As shown in FIG. 5, the network analyzer 3 has a signal supplyingcircuit 13 and a measuring circuit 14.

The signal supplying circuit 13 is constituted in such a manner thatinput signal of alternating current is able to be outputted togetherwith changing the frequency.

The measuring circuit 14 is constituted in such a manner that, on thebasis of output signal of the quartz oscillator 7 and input signaloutputted from the signal supplying circuit 13, electricalcharacteristics such as phase and resonance frequency of the quartzoscillator 7 are able to be measured and outputted to the computer 4.

The computer 4 is constituted in such a manner that, on the basis of themeasured electric characteristics such as frequency characteristic ofthe quartz oscillator 7, reaction rate, etc. of the component in thesample solution are able to be determined whereby analysis of thecomponent is able to be done.

A procedure for the analysis of reaction state of the specific componentin the sample solution such as blood with a reaction material 12 locatedon the surface of the quartz oscillator 7 by the biosensor device 1having the above-mentioned constitution will now be illustrated ashereunder.

Firstly, as shown in FIG. 6, a sample solution 8 is charged into acylindrical cell 15 having a quartz oscillator 7 on the bottom, thenetwork analyzer 3 is driven under the state where the quartz oscillator7 is dipped in the sample solution 8 and control signal is outputtedfrom the computer 4. On the basis of the outputted control signal, theinput signal outputted from the signal supplying circuit 13 is outputtedto the sensor part 2 via the cable 5.

When the input signal is supplied from the signal supplying circuit 13to the quartz oscillator 7, the quartz oscillator 7 to which the inputsignal is supplied outputs the output signal corresponding to the inputsignal. As shown in FIG. 5, the output signal is outputted to thenetwork analyzer 3 via the cable 5 and is inputted to the measuringcircuit 14 in the network analyzer 3. Then the measuring circuit 14detects the signal intensity (corresponding to the amplitude ofoscillated frequency in this case) of the output signal of the quartzoscillator 7 to which the input signal is supplied.

The above signal supplying circuit 13 changes the frequency of the inputsignal within a predetermined frequency range and the measuring circuit14 detects the signal intensity of the output signal whenever thefrequency of the input signal changes. As a result, the relation betweenthe frequency of the input signal and the signal intensity of the outputsignal is determined.

As such, the measuring circuit 14 measures the resonance frequency ofthe quartz oscillator 7 and the resulting resonance frequency of thequartz oscillator 7 is outputted to the computer 4 via the cable 6.After a predetermined period of time elapses, the computer 4 stops thesupply of the signal.

In this embodiment, the above measurement is firstly carried out by afundamental mode frequency of the quartz oscillator 7 and the resonancefrequency by the fundamental mode frequency is determined. On the basisof the measured resonance frequency, the same measurement as in thealready-mentioned measurement using the fundamental mode frequency isconducted using the n-th overtone resonance frequency.

Measurement of at least any of mass load, viscoelasticity load andviscous load which are properties of the substance to be measured iscarried out using the above-illustrated method.

This device also gives a graphic display where each of the difference inthe changing amounts in F₂ among the above-mentioned frequencies (ΔF₂)and the difference in one half of the changing amounts of F₁, F₂ amongthe above-mentioned frequencies (Δ(F₁−F₂)/2) is shown on the display ofthe computer 4.

EXAMPLES

An example of the preset invention will be mentioned as follows.

A quartz oscillator where resonance frequency was 27 MHz was dipped in acell filled with a buffer (a biochemical buffer where main componentstherein were NaCl and KCl) and avidin, 30 mer b-DNA and 30 mer c-DNAwere successively bonded thereto.

At that time, frequencies F₁ and F₂ giving a half value of theconductance G (G/2) when the quartz oscillator was oscillated with afundamental mode frequency (27 MHz) and a third overtone mode frequency(81 MHz) were used and changing amount of ΔF₂ and changing amount ofΔ(F₁−F₂)/2 in each case was measured (FIG. 7).

When the value of Δ(F₁−F₂)/2 greatly varies, it is noted from the aboveformula (6) that changes in viscosity and changes in viscoelasticity aregreat whereby it is found that changes in viscosity and changes inviscoelasticity are great when b-DNA is added.

FIG. 8 is the result where the changing amount of ΔF₂ and the changingamount of Δ(F₁−F₂)/2 are applied to a Voight model and calculation isconducted on the basis of the above formulae (5) and (6) while FIG. 9 isthe result of the calculation in a Maxwell model.

From those results, it is noted that changes in viscosity and changes inviscoelasticity which are properties of the additive is able to bemeasured separately from mass load. Further, when the case where avidinis bonded to the surface of the gold electrode of the quartz oscillatorand the case where c-DNA is bonded to b-DNA are compared, there is nobig change in viscoelasticity as compared with mass load but, when b-DNAis bonded to avidin, the rate of changing amount of frequency byviscoelasticity is great as compared with other bonds. Thus, it is notedthat big changes in viscoelasticity is resulted.

INDUSTRIAL APPLICABILITY

The present invention is able to be utilized to measurement, etc. whereinteraction and antigen-antibody reaction of biomaterials such as DNAand protein are utilized.

1. A method where property of a substance contacting to a quartzoscillator equipped with electrodes on both sides of a quartz plate ismeasured on the basis of the changes in frequency of the above quartzoscillator, characterized in that, the property of the above substanceis measured using at least two mode frequencies among the n-th overtonemode frequencies of the quartz oscillator, wherein n=1, 3, 5, . . . ,when voltage is applied between the above electrodes and using F_(1@N1),F_(2@N1) which are a set of frequencies F₁, F₂ measured by one n-thovertone mode frequency N1s, wherein F₁<F₂, giving one half of themaximum value of conductance near the resonant point by each frequency,and F_(1@N1), F_(2@N2) which are a set of frequencies F₁, F₂ measured byother n-th overtone mode frequencies, N2, wherein F₁<F₂ giving one halfof the maximum value of conductance near the resonant point by eachfrequency, wherein the values of ω²ρ₂η₂h₁/μ₁ and C are determined fromthe measured value:(ΔF_(2@N1)/N1−ΔF_(2@N2)/N2)/(Δ(F_(1@N1)−F_(2@N1))/2N₁^(1/2)−Δ(F_(1@N2)−F_(2@N2))/2N₂ ^(1/2)) wherein ΔF_(2@N1)/N1−ΔF_(2@N2)is expressed by the expression 9′, and Δ(F_(1@N1)−F_(2@N1))/2N₁^(1/2)−Δ(F_(1@N2)−F_(2@N2))/2N₂ ^(1/2)) is expressed by the expression10′:(N1·(1+N1·C)/(1+(N₁·C)²)−N2·(1+N₂·C)/(1+(N₂·C)²))·ω²ρ₂η₂h₁/μ₁  [Expression9′] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer,(−(N1)^(3/2)/(1+(N1·C)²)−(N2)^(3/2)/(1+(N2·C)²))·ω²Σ₂η₂h₁/μ₁  [Expression10′] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer, and after the values of ω²ρ₂η₂h₁/μ₁ and C are determined, themass load, the viscoelasticity term 1, the viscous load and theviscoelasticity term 2 are obtained from the formula 7′, formula 7″,formula 8′ and formula 8″, respectively:the mass load=ΔF _(2N) /N−(1+C·N)·Nω ²ρ₂η₂ h ₁/μ₁(1+C ² N ²)  [Formula7′] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer,the viscoelasticity term 1=ΔF _(2N) /N ²+(the mass load)/N,  [Formula7″]the viscous load=Δ(F _(1N) −F _(2N))/2·N ₁ ^(1/2) +N ^(3/2)ω²ρ₂η₂ h₁/μ₁·(1+C ² N ²)  [Formula 8′] wherein ω is angular frequency, η_(n) isviscosity of the liquid, ρ_(n) is density of the liquid, h_(n) is filmthickness and n is n-th layer,the viscoelasticity term 2=Δ(F _(1N) −F _(2N))/2·N ²+(the viscousload)·N.  [Formula 8″]
 2. A measuring device using the measuring methodmentioned in claim 1, characterized in that, each of the difference inthe changing amount of F₂ between the above frequencies and thedifference in one half of the difference in F₁ and F₂ among the abovefrequencies is expressed by a graph generated on a computer screen.
 3. Amethod where property of a substance contacting to a quartz oscillatorequipped with electrodes on both sides of a quartz plate is measured onthe basis of the changes in frequency of the above quartz oscillator,characterized in that, the property of the above substance is measuredusing at least two mode frequencies among the n-th overtone modefrequencies of the quartz oscillator, wherein n=1, 3, 5, . . . , whenvoltage is applied between the above electrodes and using F_(1@N1),F_(2@N1) which are a set of frequencies F₁, F₂ measured by one n-thovertone mode frequency, N1, wherein F₁<F₂, giving one half of themaximum value of conductance near the resonant point by each frequency,and F_(1@N2), F_(2@N2) which are a set of frequencies F₁, F₂ measured byother n-th overtone mode frequencies, N2, wherein F₁<F₂ giving one halfof the maximum value of conductance near the resonant point by eachfrequency, wherein the values of ω²ρ₂η₂h₁/μ₁ and C are determined fromthe measured value:(ΔF_(2@N1)/N1−ΔF_(2@N2)/N2)/(Δ(F_(1@N1)−F_(2@N1))/2N₁^(1/2)−Δ(F_(1@N2)−F_(2@N2))/2N₂ ^(1/2)) whereinΔF_(2@N1)/N1−ΔF_(2@N2)/N2 is expressed by the expression 9′, and:Δ(F_(1@N1)−F_(2@N1))/2N₁ ^(1/2)−Δ(F_(1@N2)−F_(2@N2))/2N₂ ^(1/2)) isexpressed by the expression 10′:(N1·(1+N1·C)/(1+(N₁·C)²)−N2·(1+N₂·C)/(1+(N₂·C)²))·ω²ρ₂η₂h₁/μ₁  [Expression9′] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer,(−(N1)^(3/2)/(1+(N1·C)²)−(N2)^(3/2)/(1+(N2·C)²))·ω²Σ₂η₂h₁/μ₁  [Expression10′] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer, and after the values of ω²ρ₂η₂h₁/μ₁ and C are determined, then-th, mass load, the n-th viscoelasticity term 1, the n-th viscous loadand the n-th viscoelasticity term 2, which are measured by the n-thovertone mode frequency, are obtained from the formula 7′″, formula 7″″,formula 8′″ and formula 8″″, respectively:the n-th mass load=ΔF ₂ N−(1+C·N)·N ²ω₁ρ₂η₂ h ₁/μ₁(1+C ² N ²)  [Formula7′″] wherein ω is angular frequency, η_(n) is viscosity of the liquid,ρ_(n) is density of the liquid, h_(n) is film thickness and n is n-thlayer,the n-th viscoelasticity term 1=ΔF_(2N)+(the n-th mass load),  [Formula7″″]the n-th viscous load=Δ(F _(1N) −F _(2N))/2+N ²ω²ρ₂η₂ h ₁/μ₁−(1+C ² N²)  [Formula 8′″] wherein ω is angular frequency, η_(n) is viscosity ofthe liquid, ρ_(n) is density of the liquid, h_(n) is film thickness andn is n-th layer,the n-th viscoelasticity term 2=Δ(F _(1N) −F _(2N))/2+(the n-th viscousload).  [Formula 8″″]